SOLUTION: i cant figure this one out it confuses me My digits are the same. their sum is 3 less than their product. Who am i?

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Question 207669: i cant figure this one out it confuses me
My digits are the same. their sum is 3 less than their product. Who am i?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm assuming that this number is a two digit number.


Let d = value of unknown digit


Since all the digits are the same, this means that the number is n=10d%2Bd where 'n' is the unknown 2 digit number.


Because "their sum is 3 less than their product", we know that d%2Bd=d%2Ad-3


d%2Bd=d%2Ad-3 Start with the given equation.


2d=d%2Ad-3 Combine like terms.


2d=d%5E2-3 Multiply


0=d%5E2-2d-3 Subtract 2d from both sides.


Notice that the quadratic d%5E2-2d-3 is in the form of Ad%5E2%2BBd%2BC where A=1, B=-2, and C=-3


Let's use the quadratic formula to solve for "d":


d+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


d+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-3%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-2, and C=-3


d+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-3%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


d+=+%282+%2B-+sqrt%28+4-4%281%29%28-3%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


d+=+%282+%2B-+sqrt%28+4--12+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-3%29 to get -12


d+=+%282+%2B-+sqrt%28+4%2B12+%29%29%2F%282%281%29%29 Rewrite sqrt%284--12%29 as sqrt%284%2B12%29


d+=+%282+%2B-+sqrt%28+16+%29%29%2F%282%281%29%29 Add 4 to 12 to get 16


d+=+%282+%2B-+sqrt%28+16+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


d+=+%282+%2B-+4%29%2F%282%29 Take the square root of 16 to get 4.


d+=+%282+%2B+4%29%2F%282%29 or d+=+%282+-+4%29%2F%282%29 Break up the expression.


d+=+%286%29%2F%282%29 or d+=++%28-2%29%2F%282%29 Combine like terms.


d+=+3 or d+=+-1 Simplify.


So the possible solutions are d+=+3 or d+=+-1


However, it doesn't make sense to have a negative digit. So the only answer is d=3


This means that the unknown digit is 3 which would make the 2 digit number of 33.